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Teacher's Guide 



All Sunburst material is copyrighted. However, Sunburst does give the purchaser the 
following permissions: 

• You have permission to reproduce any student worksheets in this guide for your 
classroom use. You should not, however, copy the whole guide. 

• If you purchased this program for one computer, you may use it on a single 

• If you wish to use this software on multiple computers, you must purchase the 
right to do so from Sunburst. Call and ask for lab pack/site licensing prices. 

• You have permission to use lab packs/site licenses within one site. You do not, 
however, have permission to divide the package and use the software in more 
than one site. 


Product Manager 

Project Editor 


Software Graphics 

Quality Control 

Desktop Publisher 


ThomasC. O'Brien, Ph.D. 

Paul Kronmeyer 
Joan Jacobsen 

Carrie Gerard i 

Salti re Software, Inc. 

Carrie Gerard i 

Gregory Sill ins 

Carrie Gerardi 

Emilie Rappoport 

Copyright © 1998 Sunburst Communications, Inc. 

TI-GRAPH LINK is a trademark of Texas Instruments Incorporated. 

Windows and Windows NT are registered trademarks of M icrosoft Corporation 

in the U nited States and/or other countries. 

For more information or for a free catalog, call or write: 

Sunburst Communications, Inc. 

101 Castleton Street 

Pleasantville, NY 10570 

Toll-free: 1-800-321-7511 
Or call collect: 914-747-3310 

Visit us on the Web: www.SU N BU 

Table of Contents 

A bout the A uthor 1 

I ntroduction 3 

Getting Started 

H ardware and Software Requirements 5 

Installing Puzz/e 7an/cs on a T 1-73 5 

Program Description 

Welcome to Puzzle Tanks 7 

Finding Your Way A round PuzzleTanks 9 

Scoring 10 

How to Play 10 

Levels of Play 10 

Impossible Problems 12 

Champion List 12 

Trouble Shooting 

Error Recovery Instructions for the T 1-73 15 

M iscellaneous 16 

Technical Support 16 

About the Author 

Thomas C. O'Brien, Ph.D. 

Thomas C. O'Brien is a former professor at Southern Illinois University, 
Edwardsville, Illinois. His work in education is three-fold: teacher education, 
curriculum development and research on children's thinking. Asa researcher, he 
has studied the growth of mathematical ideas in subjects from pre-school to 
medical school and law school. Asa teacher, he has worked with students from 
the seventh grade through graduate school. Asa curriculum developer, he has 
written twelve math-problem books for children, as well as written and edited 
some eighty papers on children's thinking and education published through the 
Teachers' Center Project. 

In addition, Dr. O'Brien has published and delivered some 100 papers on chil- 
dren's thinking, mathematics education, intellectual development and educa- 
tional change. H is papers and presentations have taken place in the U nited 
States, Canada, Great Britain, Holland, France, Switzerland, Hungary and 
Brazil. Dr. O'Brien was named a North Atlantic Treaty Organization (NATO) 
Senior Research Fellow-in-Science in 1978. He received his bachelor's degree 
from lona College, New Rochelle, NY, and his Ph.D. from New York University. 

Other Sunburst programs designed by Thomas O'Brien include: Teasers by 
Tobbs, Tobbs L earns A Igebra, TheK ing's R ule, TheR oyal R ules, B lockers and 
Finders, Blockers and Finders II, W inker's W orld of Patterns, Winker's World of 
N umbers, M ore Teasers by Tobbs, Teasers by Tobbs with Integers and L abel L and. 



Suppose you have the following problem: 

You have two tanks, one of which holds 5 quarts and the other 6. 
You have an infinite supply of Wonder Juice and a holding con- 
tainer into which you could pour the contents of the tanks. You 
must use the original tanks — the 5 and 6 — to make 11 quarts 
of Wonder Juice. 

Easy. Fill the 5 and the 6 and empty them into the holding tank. 

Why do a problem like this? Such a problem calls for children to develop and/or 
apply addition skills and to view addition in its very essence. Addition is not 
reciting responses from memory. Addition involves combining things. 

Here's another problem: 

Suppose you have the same 5 and 6 tanks and this time you need 
2 quarts of Wonder Juice. Not so easy, is it? You could fill the 6 
and pour it into the 5, thus leaving 1. Save the 1 in the holding 
container. Then empty the 5. Can you finish the problem? 

This isn't an exercise in addition facts. What is it? It's problem solving, one of 
the most important abilities one can have. 

Problem solving takes place when one reassembles (or creates) actions and ideas 
to achieve a goal in a new situation. We are all problem solvers every day, and 
we are all more or less successful at problem solving. But problem-solving abili- 
ties are too important to leave to chance and the random experiences of every- 
day life. Problem solving needs special attention. 

M uch of the school curriculum purports to promote problem solving. The 
National Council of Teachers of Mathematics chose problem solving as its issue 
for teachers to pursue in the 1980's. Present-day school children will live most of 
their lives in the twenty-first century. What new issues will they face? No doubt, 
facts will be important to them, but they'll meet novelty and challenge and 
opportunities presently unknown to us. (Some of you are old enough to remem- 
ber when Dick Tracy's wrist radio was unspeakably futuristic. Do you remember 
— i t's just over 35 years ago — when a man on the moon was unthinkable? Can 
you think back to the time when a computer in a private home was not so com- 

A major aspect of life is novelty — dealing with new situations for which you've 
not been programmed. What do you do? You create your own solutions. You 
become a problem solver. Problem solving is, and should be, a major objective 
in schools and the home. 


But problem solving in math textbooks is often falsely named. "Problems" in 
most math textbooks aren't really problems. They are computational exercises 
disguised in words: "Two boys each ate 4 hamburgers...." Such activities are triv- 
ial so far as problem solving is concerned, and they are trivial from the point of 
view of utility. I haven't had to solve a "word problem" in the last thirty years of 
my adult life, but during the same time, I have met and solved dozens of prob- 
lems every day. 

What does problem solving involve? H ofstadter says it nicely in Godel, Escher, 

• to respond to situations flexibly; 

• to take advantage of fortuitous circumstances; 

• to find similarities between situations despite differences that may 
separate them; 

• to synthesize new concepts by taking old concepts and putting them 
together in new ways; and 

• to come up with novel ideas. 

Puzzle Tanks then, is concerned with problem solving in the H ofstadter sense. It 
is concerned with children's ability — and willingness and confidence— to 
make sense out of a situation and devise alternatives to reach a goal. The con- 
struction of alternatives, not the repeating of pat formulas, is what thinking and 
problem solving are all about. 

About PuzzleTanks 

How does PuzzleTanks create a good educational environment? 
It deals with issues that are important. Problem solving is important. 

It enables the student to be active— to invent ideas, to try them out and, if 
necessary, to revise them. The very nature of PuzzleTanks is that players invent 
solutions and revise them. M istakes, by the way, are okay. (Can you conceive of 
an infant learning to walk without lots of falls at the beginning?) 

It adds diversity. At each level of PuzzleTanks, what worked for the last problem 
is unlikely to work for the next. Further, every individual problem has many dif- 
ferent solutions. There is no such thing as "the one right way." 

It has a wide variety of entry points and a high ceiling. PuzzleTanks starts with 
very simple problems, such as the 5 + 6 = 11 task described earlier, but the 
higher level problems have stumped some very bright, well educated people. 

Thus, PuzzleTanks puts kids in real problem-solving situations with real lifelong 


Getting Started 

Hardware and Software Requirements 

Make sureyou havethe following items: 

• TI-GRAPH LINK™ computer-to-calculator cable. If you do not 
haveaTI-GRAPH LIN K cable, call Sunburst, or order the cable 
online at the T I Accessory Store ( 

• Connecting TI-GRAPH LIN K cable adapter, 9-pin to 25-pin, if 

• Computer with Windows® 3.1x or Windows® 95/98 installed. (A 
Windows NT® version will soon be available.) 

• Puzzle Tanks software for the T I -73 on disk. 

• A T 1-73 calculator. 

Thingsto Check BeforeYou Begin 

To make sure the batteries in your T 1-73 are in good working condition, turn on 

your T 1-73. If there is a low- battery message on the screen, turn the T 1-73 off 

and follow the battery replacement procedure in Appendix C of your T 1-73 


Before you load Puzzle Tanks into your T I -73, verify that sufficient free space 
exists in your application memory space by entering 2nd M EM, 3:Check APPs. 
The first line indicates the number of free spaces available. Most applications 
will take up only one space. Seethe Memory is Full instructions in the Trouble 
Shooting Section for details about deleting applications. 


The TI-73 
may briefly display 
a "defragmenting" 
message. This 
simply means the 
calculator is 
preparing for 

Installing PuzzleTanks on aTI-73 

1. M ake sure the T I -G RA PH LINK cable is firmly connected to the calculator 
and the computer and the calculator is at the home screen. 

2. Start Windows and close all desktop applications that may be running 
(another running application could interfere while Puzzle Tanks is updat- 
ing your TI-73). 

3. Select Run from the File menu (Windows® 3.1) or Run from the Start 
menu (Windows® 95). In the Run dialog box, type 
C :\ directoryname\ ti73puzz.exe (where directoryname is the directory to 
which you downloaded the Puzzle Tanks file) and then click OK. 

4. Follow the on-screen instructions to complete the installation. 

Important: DO NOT interrupt the installation process. If any errors are 
encountered during the installation, follow the instructions. Error Recovery 
instructions are also described in the Trouble Shooting Section of this guide. 

Program Description 

Welcome to PuzzleTanks 

The following section takes you through a sample game of PuzzleTanks. 

After installation is complete, find and press the 
A PPS button located on the calculator below and 
to the left of the down arrow. The Applications 
screen will appear. 



Names may 
be a maximum of <3 
characters long. 
Also, you may use 
the number keys 
when entering a 




On the Applications screen use the arrow keys to 
scroll down and highlight PU ZTA N KS or press 
the number that corresponds with the PU Z- 
TAN KS. In the above example, PuzzleTanks is the 
third application on the calculator. In this case 
pressing 3 will launch the application. 

At the credits screen press any key to continue. 
You will be prompted to enter your name. 

fu :: l e THriKi" 

EnUr your nam: 

S T L! V H X Y Z ■■ 

addTdel I CLR | " TDIinE 

U se the arrow keys to navigate among the letters 
on the alphabet chart. The ADD option in the 
menu bar allows you to select the highlighted let- 
ters. The DEL option in the menu bar allows you 
to delete the last letter selected. nee you have 
finished entering your name, use the DON E 
option in the menu bar to go to the M ain screen. 

Program Description 

U se the arrow keys and the enter key to select the level of play you'd like to 
start with. To familiarize yourself with the game, you may want to choose the 
Beginner level first. 


ISEGinnER | 






Once you choose the level you want, a problem will be presented. After you've 
read the problem, press any key to begin solving it. 


You always 
have an unlimited sup- 
ply of liquid with which 
to fill the tanks. 







You n««d 

50 quarts 

of Pow«r Punch. 

Tht lanks hold 
9 and 7 quarts. 

Yyhw any U*y... 

A solution to this problem is shown in the following steps: 

(iiliiL 50 


aQAL 50 


GOAL 50 


Graphic representation of 
the problem. 

Fill the 9-quart tank. 

Move the contents of the 
9-quart tank into the truck. 


SEAL 50 


Fill the 7-quart tank 

£[ihi. 50 


Move the contents of the 7- 
quart tank into the truck. 

GOAL 50 

) B47\ |?feBU(^ACK 

Fill the 7-quart tank 2 more 
times, each time moving the 
contents to the truck. 


Program Description 

The congratulatory screen will appear when you solve the problem. 


B) * 




IUU dono CARRIE!! 
YOU ™< xOLir 

Pow^r Punch. 

Pr«s any k4tv... 

k 20 J 

W hen you feel you have mastered the level at which you started, move on to 
the next level for a greater challenge. 

Finding Your Way Around PuzzleTanks 

You will use the main menu bar located at the bottom of the screen to interact 
with PuzzleTanks. The five keys directly below the game screen (hereafter 
referred to as the M aster keys) correspond directly to the five items in the menu 
bar. Filling and emptying tanks, or moving liquid between tanks, can all be 
accomplished using these keys. For example, pressing the Y= key on the calcula- 
tor will activate the FILL option in the menu bar. 

Below is a description of each of these options. 

• FILL causes a new menu bar to appear with options to fill either of 
the tanks with liquid. BACK is provided to take you back to the main 
menu bar if you do not wish to fill any tanks after all. 

• MOVE causes a new menu bar to appear with options to move liquid 
from one tank to another, or to move the liquid from one tank into the 
truck. BACK is provided to take you back to the main menu bar if you 
do not wish to move any liquid. 

• EMTY causes a new menu bar to appear with options to empty either 
of the tanks that contain liquid. BACK is provided to take you back to 
the main menu bar if you do not wish to empty either of the tanks. 

• IMP Indicates if a problem is impossible or not. A congratulatory 
message will appear if you are correct. If the problem is possible, a mes- 
sage will appear indicating the problem can be solved. In either case, you 
will be charged one try in the Tries section of the screen. 

• OPTS activates a dialog box offering the following choices: either 
starting a new game or replaying the same game, going to the main 
menu, getting directions, viewing the champion list, or quitting the 

Program Description 



The program keeps track of the number of moves or "tries" used to solve each 
problem. That number is shown along with the goal amount in a box located on 
the right side of the game screen. In the Champion level, this number is record- 
ed, and the player who solves the problem in the least number of tries is listed as 
the champion for that problem. 

How to Play 

I n Puzzle Tanks, you are given the option to choose from four levels of play: 
Beginner, Expert, Master and Champion. Each level increases in difficulty. The 
tanks are chosen at random from 1 to 9 units; the goal amount is also chosen at 

First, enter your name; then select a level of play. After you have selected a 
level of play, you will be presented with a problem. Press any key to continue. 
A graphic illustration of the elements in the problem will be displayed on the 
screen. You can attempt to solve the problem by filling tanks, emptying tanks, 
and moving liquids between the tanks or into the truck (depending on the level 
of play) by using the options in the menu bar. 

Levels of Play 

Beginner Level 

In the Beginner level, the problems involve simple addition, subtraction and 

multiplication. Here is an example: 

Given a 9 and a 3, make 12 
Given a 9 and a 3, make 6 
Given a 9 and a 3, make 27 
Given a 9 and a 3, make 21 


(M ultipl ication. Three 9's.) 
(M ulti pi ication and addition-Two 
9's plus a 3.) 

In summary, if one tank holds "a" and the other holds "b," Beginner level prob- 
lems use the following formulas: 

• a+b 

• a-b 

• kx a (e.g., 3 x a) 

• k x a + c x b (e.g., 2 x a + 6 x b— two of one tank and 
six of another tank will fill the truck) 

Program Description 


Expert Level 

In the expert level the problems are more challenging. Suppose you had tanks 

holding units of 6 and 5, and the goal is 8. There could be a couple of different 


You could do 6 - 5 eight times, emptying each of the remaining 
units into the truck. 

Or you could do 6 + 1 + 1. 
Can you think of other solutions? 

M aster L evel 

A t the M aster level, the situation changes completely— there's no truck for stor- 
age! ne must obtain the target amount with only the two tanks provided. 
H ere's an example of a M aster problem: 


A solu- 
tion is recog- 
nized whether 
it's in one tank 
or shared 
between the 
two tanks. 






You nttd 

i <iuar< 

q$ udd nil. 

Th« tanks hold 
3 and ! i quarts. 

rr£SS any k«y... 




Yoli havt only 2 
tanks to work with. 

You must obtain 

th« i <iuart 

usinS! th« 2: 'tanks. 

rr«ss any k«y... 

Here is a solution: 

H < 

HftL 1 

— Tri«s — I 

TJ — 


1 J 



Graphic representation of 
the problem. 

!=! aQAL i 

— Tri«S — I 


Fill the 9-quart tank. 

M aHAL 1 

— Tri«S — I 

TJ ■ — ' — 


Move the contents of the 9- 
quart tank to the 4- quart 

ri GDAL i 

— Tri«S — 


Empty the 4-quart tank. 

ri GDmL i 


— Trks — 
L l 

TJ — 1 — ' — 

fzllThdveTehtyI xhfIdpts 

Move the contents of the 9-quart 
tank into the 4-quart tank. 



! T 1 Wis 

Empty the 4-quart tank and 
you are left with 1 quart! 

Program Description 


The goal wasl, so the problem was solved in five steps. Is there a solution with 
fewer steps? 

C hampion L evel 

Champion is the most challenging level of play. At this level, you may be pre- 
sented with a problem that has already been solved by another player who is the 
champion for that problem. This gives you the opportunity to try to solve the 
problem in as many or fewer steps than your "opponent." 

If there is no champion for the problem, it will be noted on the opening screen 
describing the problem: "No one holds the championship." If there is a champi- 
on for the current problem, the opening screen will give you the name of the 
player holding the current championship and how many tries were required to 
solve the problem. 

If you succeed in getting the better score or tying the current champion, then 
you become the new champion, and the score is recorded on the C hampion list. 

Impossible Problems 

To add an extra challenge to the Expert and M aster levels of play, some of the 
problems are impossible to solve. For example, try to use a 2 and a 6 to make 1. 
It can't be done. W ith a 2 and a 6, only 2, 4, 6, 8, 10, etc., are attainable goals. 
In general, if the two tanks share a divisor (e.g., tanks of 3 and 9, 6 and 8, 2 and 
10), only multiples of that divisor are possible. If the tanks share no common 
divisor other than 1, the sky's the limit! For example, tanks of 3 and 5 can be 
used to obtain 1, 2, 3, 4, etc. 

Champion List 

The Champion List is accessible from the OPTS menu in the menu bar of each 
game. It can be accessed anytime during or at the end of a game. The Champion 
List holds and stores the names of the "champs" who were able to correctly 
answer the Champion Level problems. The list contains the goal and tank sizes, 
the names of the champs and how many tries they used to complete the prob- 

nu CHAiiP 
ft£! CHAMp 
liEJ Ch&HP 

tlSyTclrt r i<a1i<i: 


Program Description 

You can scroll through the Champion List using the arrow keys on the calcula- 
tor. The menu bar in the Champion List screen contains 3 options; PLAY, CLR 
and CAN CL. If you see a game you would like to play, use the arrows to high- 
light that game and select PLAY from the menu bar. The game will then open 
and you will have a chance to become the new champion. To reset any of the 
games in the Champion List back to No Champ simply use the arrow keys to 
highlight the game and select CLR from the menu bar. If you only went into 
the Champion List to look around, use the CAN CL option in the menu bar to 
take you back to the screen where you were previously. 


Trouble Shooting 

Error Recovery Instructions For the T 1-73 

Communication Error 

This error indicates the Flash Installer is unable to communicate with the 
T 1-73. The problem is usually associated with theTI-GRAPH LIN K ™ cable and 
its connection to the T 1-73 and/or to the computer. Make sure the cable is firm- 
ly pushed into the calculator and the computer. 

If this does not correct the problem, try a different T I -GRAPH LIN K cable and 
reboot your computer. If you continue to get this error, please contact 
1-800-TI-CARES (see Technical Support). 

M emory is F ull 

This download error appears when the T 1-73 contains one to four applications 
that occupy the available 64K of space. In order to make room for another 
application, you must delete one from the T 1-73. Before deleting an application 
from the T 1-73, you can back it up by using the Windows Backup A pp command 
in TI-GRAPH LIN K for the T 1-73. Once saved, you can reload it to the 
TI-73 later using T l-G RA PH LINK. 

Expiration D ate R eached 

The application has reached its expiration date and can no longer be used. 
Please contact 1-800-TI-CARES (see Technical Support). 

M iscellaneous E rror Received 

W rite down the error code displayed in the dialog box and contact 
1-800-TI-CARES (see Technical Support). 

Checksum Error 

Exit the installer and try it again. If this problem persists, contact 
1-800-TI-CARES (see Technical Support). 

Low Battery Condition 

It's a good idea to make sure that you have sufficient battery power prior to 
attempting a download. Low battery indication is shown on the initial screen. If 
you receive this error during an installation, change the batteries before trying 


If you obtain new or upgraded software for your T I -73, you may need to provide 
your current software version and/or the serial number of your unit. It is also 
good to know your version number in case you have difficulties with your T 1-73 
and need to contact technical support. Knowing the software version may make 
it easier to diagnose the problem. 

Knowing the available number of application spaces in advance helps you better 
manage your application downloads. 

Verify M aintenance U pgrade Version 

On the T I -73, enter 2nd, Mem, l:About. The version number has the format 

Verify Application Version number 

On the T 1-73, select A PPS. Select the appropriate application and press 
ENTER. The version number of the application appears on the initial screen. 

Verify Serial N umber 

On the T 1-73, enter 2nd, Mem, l:About. The serial number appears on the line 
beneath the product ID number. 

C heck A mount of Flash A pplication Free Space 

n the T 1-73, select 2nd, M EM , 3:C heck A PPs. T he number to the right of 
"Spaces Free:" indicates the number of spaces available for applications. Each 
application requires one space. There are a maximum of four free spaces. 

Technical Support 

For questions concerning the installation of PuzzleTankson your T 1-73 
or for questions concerning the T 1-73 calculator, contact Texas Instruments 
Customer Support. 

C ustomers in the U .S. t C anada, Puerto Rico and the Virgin Islands 
Send use-mail 
Call us at 1-800-TI-CARES (1-800-842-2737) 

C ustomers outside theil .S. f C anada, Puerto Rico and the Virgin Islands 
Send use-mail